A010767 Decimal expansion of 4th root of 2.
1, 1, 8, 9, 2, 0, 7, 1, 1, 5, 0, 0, 2, 7, 2, 1, 0, 6, 6, 7, 1, 7, 4, 9, 9, 9, 7, 0, 5, 6, 0, 4, 7, 5, 9, 1, 5, 2, 9, 2, 9, 7, 2, 0, 9, 2, 4, 6, 3, 8, 1, 7, 4, 1, 3, 0, 1, 9, 0, 0, 2, 2, 2, 4, 7, 1, 9, 4, 6, 6, 6, 6, 8, 2, 2, 6, 9, 1, 7, 1, 5, 9, 8, 7, 0, 7, 8, 1, 3, 4, 4, 5, 3, 8, 1, 3, 7, 6, 7
Offset: 1
Examples
1.189207115002721066717499970560475915292972092...
References
- Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 5.23, p. 407.
Links
- A.H.M. Smeets, Table of n, a(n) for n = 1..20001 (first 1000 digits from Vincenzo Librandi).
- Jean-Paul Allouche, Henri Cohen, Michel Mendès France, and Jeffrey O. Shallit, De nouveaux curieux produits infinis, Acta Arithmetica, Vol. 49, No. 2 (1987), pp. 141-153; alternative link.
- Simon Plouffe, 2^(1/4) or sqrt(sqrt(2)) to 20000 digits.
- Simon Plouffe, 2^(1/4) to 1024 places.
- Nikita Sidorov and Boris Solomyak, On the topology of sums in powers of an algebraic number, arXiv:0909.3324 [math.NT], 2009-2011.
- David Terr and Eric W. Weisstein, Pisot Number.
- Eric Weisstein's World of Mathematics, Algebraic integer.
- Index entries for algebraic numbers, degree 4.
Programs
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Mathematica
RealDigits[N[2^(1/4),200]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jan 24 2012 *)
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PARI
sqrtn(2,4) \\ Charles R Greathouse IV, Apr 14 2014
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PARI
weber(I) \\ Charles R Greathouse IV, Feb 04 2015
Formula
Equals Product_{k>=0} (1 + (-1)^k/(4*k + 3)). - Amiram Eldar, Jul 25 2020
Equals Product_{k>=0} ((2*k+1)/(2*k+2))^(A000120(k)*(-1)^A000120(k)) (Allouche et al., 1987). - Amiram Eldar, Feb 04 2024
Comments